Bayesian estimation for time-series regressions improved with exact likelihoods

Abstract

We propose an estimation procedure for time-series regression models under the Bayesian inference framework. With the exact method of Wise [Wise, J. (1955). The autocorrelation function and spectral density function. Biometrika, 42, 151–159], an exact likelihood function can be obtained instead of the likelihood conditional on initial observations. The constraints on the parameter space arising from the stationarity conditions are handled by a reparametrization, which was not taken into consideration by Chib [Chib, S. (1993). Bayes regression with autoregressive errors: A Gibbs sampling approach. J. Econometrics, 58, 275–294] or Chib and Greenberg [Chib, S. and Greenberg, E. (1994). Bayes inference in regression model with ARMA(p, q) errors. J. Econometrics, 64, 183–206]. Simulation studies show that our method leads to better inferential results than their results.

Keywords:

• Autoregressive process
• Exact likelihood
• Markov chain Monte Carlo
• Partial autocorrelations

Acknowledgements

The authors thank Nan-Yu Wang for initial simulation study. C. W. S. Chen and Jack C. Lee acknowledge research support from National Science Council of Taiwan grants NSC91-2118-M-035-002 and NSC91-2118-M-009-002, respectively.